Hodge-Gaussian maps
Let $X$ be a compact Kahler manifold, and let $L$ be a line bundle on $X.$ Define $I_k(L)$ to be the kernel of the multiplication map $ Sym^k H^0 (L) o H^0 (L^k).$ For all $h leq k,$ we define a map $ ho : I_k(L) o Hom (H^{p,q} (L^{-h}), H^{p+1,q-1} (L^{k-h})).$ When $L = K_X$ is the canonical bundle, the map $ ho$ computes a second fundamental
Colombo, Elisabetta et al.
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